Breathing Charge Density Waves in Intrinsic Josephson Junctions

We demonstrate the creation of a charge density wave (CDW) along a stack of coupled Josephson junctions in layered superconductors. Electric charge in each superconducting layer oscillates around some average value, forming a breathing CDW. We show the transformation of a longitudinal plasma wave to CDW in the state corresponding to the outermost branch. Transitions between different types of CDW's related to the inner branches of current voltage characteristics are demonstrated. The effect of the external electromagnetic irradiation on the states corresponding to the inner branches differs crucially from the case of the single Josephson junction. The Shapiro steps in the IV-characteristics of the junctions in the stack do not correspond directly to the frequency of radiation $\omega$. The system of Josephson junctions behaves like a single whole system: the Shapiro steps or their harmonics in the total IV-characteristics appear at voltage $\sum V_l=N_R\frac{m}{n}\omega$, where $V_l$ is the voltage in $l$-th junction, $N_R$ is the number of JJ in the rotating state, and $m$ and $n$ are integer numbers.